The elements of plane trigonometry |
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Página 2
... known , X if we know the magnitudes of the perpendiculars let fall from P1 upon the lines XAX ' and YAY ' , viz . PN , and PM ( or AN1 , which is equal to PM ) . P M N N2 A NA N X Y AN1 , N1P1 , are called the co - ordinates of P ...
... known , X if we know the magnitudes of the perpendiculars let fall from P1 upon the lines XAX ' and YAY ' , viz . PN , and PM ( or AN1 , which is equal to PM ) . P M N N2 A NA N X Y AN1 , N1P1 , are called the co - ordinates of P ...
Página 58
... known from ( i ) and ( iii ) , and the triangle is determined . Now the sine of an angle is equal to the sine of its supplement , and therefore there are two angles which satisfy ( ii ) , the one greater and the other less than 90 ...
... known from ( i ) and ( iii ) , and the triangle is determined . Now the sine of an angle is equal to the sine of its supplement , and therefore there are two angles which satisfy ( ii ) , the one greater and the other less than 90 ...
Página 68
... known , - B = 1 ( B + C ) + 1⁄2 ( B − C ) - and C = ( B + C ) − 1 ( B − C ) sin A And a = c . // - determines a . } are known ; 85. The side a can be determined without previously determining sin C 68.
... known , - B = 1 ( B + C ) + 1⁄2 ( B − C ) - and C = ( B + C ) − 1 ( B − C ) sin A And a = c . // - determines a . } are known ; 85. The side a can be determined without previously determining sin C 68.
Página 73
... known . ( Figure to Ex . 2. ) At B let the angles of depression of the points D and A below a horizontal line passing through B be observed . Since such a line will be parallel to CD , BDC and BAC are equal to these angles of depression ...
... known . ( Figure to Ex . 2. ) At B let the angles of depression of the points D and A below a horizontal line passing through B be observed . Since such a line will be parallel to CD , BDC and BAC are equal to these angles of depression ...
Página 121
... known . Hymers ' Astronomy , Art . 148 . Ex . 2. In the same manner it may be shewn from Cos ( x + y ) = sin n . sin x . cos m + cos z . cos n , when y and n are very small , that n cos m y = n . 1 + - • cot x y • cot x = -n . n y 2 ...
... known . Hymers ' Astronomy , Art . 148 . Ex . 2. In the same manner it may be shewn from Cos ( x + y ) = sin n . sin x . cos m + cos z . cos n , when y and n are very small , that n cos m y = n . 1 + - • cot x y • cot x = -n . n y 2 ...
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Términos y frases comunes
A₁ AC AC angle containing Asin base C₁ centre circle coefficient cosec cosines decimal determined Diff difference digit equal errors Eucl expression formulæ given goniometric functions greater Hence increment integer last Article less m₁ magnitude mantissa measured Napier's rules nearly negative number of seconds P₁ perpendicular plane triangle planes AOB polar triangle pole polygon positive proved quantity radius Regular Polyhedron right angles right-angled triangle S₁ secants shew shewn Similarly sin A sin sines sines and cosines small angle solid angle sphere spherical excess spherical triangle SPHERICAL TRIGONOMETRY subtended subtraction tabular logarithmic tangents THEOREM triangle ABC triangle whose sides TRIGONOMETRY versin Wherefore π π
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Página 141 - Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number.
Página 10 - Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle.
Página 56 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation. The operation of finding the unknown parts is called the solution of the triangle.
Página 57 - ... the three interior angles of a triangle are together equal to two right angles.
Página 12 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 143 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 27 - For example, let it be required to prove the formula sin ( A - B) = sin A. cos В - cos A. sin В from the annexed figure, where ВАC' = A, and C'AD — В ; each angle being greater than a right angle.
Página 5 - ... stretched taut from one point to the other. The string will not lie on the parallel, but will evidently be in a plane which passes through the centre of the sphere. If the two points be on a meridian, the stretched string will lie on the meridian. By angular distance between two points on a sphere is meant the angle subtended at the centre of the sphere by the arc joining the given points. Thus in Fig. 4 the angle NOA is the angular distance of A from N.
Página 6 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Página 200 - Three circles whose radii are a, b, c touch each other externally ; prove that the tangents at the points of contact meet in a point whose distance from any one of them is (aba Nj a+b + cj 12.